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192                      ANALYTICAL MECHANICS
The British unit of power is the horse power, defined by the following equation:
1 H.P. = 33,000 ft'
= 550fUb:. sec.
1.   Show that 1 horse power equals about 746 watts.
2.  The engine of a train, which weighs 150 tons, is of 200 horse power. Find the maximum speed the train can attain on a level track if there is a constant resisting force of 15 pounds per ton.
3.  The diameter of the cylinder of a steam engine is 9 inches, and its-length 10 inches; the mean effective pressure per square inch is 90 pounds, and the number of revolutions per minute is 100.   Find the indicated horse power.
4.   Each of the 2 cylinders of a locomotive is 16 inches in diameter,, the length of the crank is 9 inches, the diameter of the driving wheels is 6 feet, the velocity of the train is 40 miles per hour, and the mean effective pressure is 75 pounds per square inch.   Find the power developed.
5.  A train weighing 125 tons moves at the rate of 50 miles an hour, along a horizontal road.   Find the power, in kilowatts, transformed by the motors of the electric engine which pulls the train.   The resistance is 10 pounds per ton.
6.   Find the horse power developed by an engine which moves a train at the rate of 30 miles an hour up an incline of 1 in 300.   The train weighs. 120 tons and there is a resistance of 15 pounds per ton.
7.  A belt traveling at the rate of 45 feet per second transmits 100 horse power.   What is the difference in tension of the tight and the slack sides of the belt.   The width of the belt is 20 inches.
8.  A 150-horse-power steam engine has a piston 18 inches in diameter which makes 100 strokes per minute.   Find the mean effective pressure of the steam in the cylinder.   The length of the stroke is 24 inches.
9.   The average flow over the Niagara Falls is 10,000 cubic meters per second.   The average height is 160 feet.   Find the power, in kilowatts, which could be generated if all the energy were utilized.
10.  A fire engine pumps water with a velocity of 125  through a
nozzle 1 inch in diameter.   Find the horse power of the engine required to drive the pump, if the efficiency of the pump is 75 per cent and the